Question

Vector V is shown in the graph below.

HELP!


Which of the following represents the linear form of v?



v= -6i -8j


v= -8i-6j


v= 6i +8j


v= 8i +6j

Answer 1

v = -8i - 6j

Explanation:

The starting point is (9, 9)

The direction of the vector is the direction of the arrowhead.

The i is the horizontal component.

The j is the vertical component.

Therefore, to go from the start to the end of the line, we need to travel negative 8 units (horizontally) and negative 6 units (vertically).

Therefore, v = -8i - 6j

Answer 2

(b) v = -8i -6j

Explanation:

The unit vectors in the x- and y-directions are i and j, respectively.

The vector v shown in the graph extends from x=9 to x=1, or (1 -9) = -8 units in the x-direction.

It extends from y=9 to y=3, or (3-9) = -6 units in the y-direction.

Represented as a sum of x- and y-vectors, that is ...

v = -8i -6j